The company is also focusing on Rhode Island, where about 7,500 customers remain without power. National Grid is also planning to send crews to Long Island, N.Y.

NStar spokesman Michael Durand said service for that utility’s customers was “back to normal.” A total of 400,000 customers were affected by the storm, he said. Most of the outages were the result of trees ­being toppled by high winds.

“The outages were widely spread across our service territory, but the suburbs west of Boston — like Weston, Sudbury, and Sherborn — were hit hard,” he said. NStar’s map of outages on its website shows few outages in Eastern Massachusetts, from Carlisle to Cape Cod.

At the peak of the storm Monday evening, National Grid, NStar, as well as the smaller utilities Western Massachusetts Electric Co. and Unitil, reported that more than 380,000 customers had lost power in the state.

Unitil — which serves 28,000 customers in four towns in Massachusetts, including Fitchburg and Lunenburg — ­reported that 5,200 customers experienced power outages. The company said restoration was completed Tuesday night.

Drew said the seemingly rapid restoration of power, compared to the days and weeks that passed before customers had power restored during Hurricane Irene, was the ­result of several improvements.

“Our damage-assessment system was improved, which ­allowed us to act more quickly and allocate crews faster,’’ she said. “Our tree-trimming operations have been ongoing, to ­reduce the number of lines damaged, and communications, which was a large concern after the last storm, ­improved with community leaders and customers.”

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